Using History as a Mirror to Set One's Clothes Straight
"Dear Professor Muller, what exactly did that bastard Manning do to you?" Shen Qi asked with great concern, as he had a deep interest in the History of Mathematics.
Shen Qi has research experience in both ancient and modern History of Mathematics.
During his second year of high school, while training with the provincial math Olympiad team, ancient Babylonian mathematics introduced Shen Qi to the vast History of Mathematics, and his interest in and research into the History of Mathematics began from that time.
Shen Qi could tell anecdotes about almost any mathematician with a bit of fame, unless that mathematician's daily life was unremarkable.
In the History of Mathematics, Shen Qi had never heard of Tony Manning, and he was very interested in learning about him.
"People are so close to each other, yet their souls are so far apart," Professor Muller sighed, recalling his New Jersey past with Tony Manning in a poignant, black-and-white documentary-like tone.
In the 1970s and 80s, Muller followed his mentor Gödel at Princeton, accompanying the mathematical Gödel during the last period of his life.
According to Muller's recollection, this was his most important period, the period of his academic maturity and formation.
Besides his academic achievements, Muller also found love and friendship during that time.
Muller fell in love with an American girl.
The American girl was kind, sexy, passionate, and beautiful. She worked as a dancer at a club and Muller. Their love blossomed quickly, and they got married just three months after they met.
At the same time, Muller met Tony Manning, an important academic partner and a muscular young American.
The two young Mathematical Research shared a high degree of consensus in their academic thinking, and they were like kindred spirits admiring each other. They successfully collaborated on many projects, and Tony Manning was once nominated as a candidate for the MacArthur Genius Grant, an award given only to scientific geniuses in the United States.
But Tony Manning had a bad habit: he loved gambling and often went to nearby Atlantic City to try his luck.
Tony Manning, a math whiz, was lucky; while others lost nine out of ten bets, he won nine.
Moreover, Manning was able to control his desires. Every time he got a thousand or two dollars, or even a few hundred dollars, he would leave the casino and then indulge in a life of pleasure.
Even with the utmost caution, an accident still occurred.
One time, Tony Manning made a mistake. He couldn't control his devilish impulse and gambled too much, losing all his savings and incurring a debt of up to $150,000 overnight.
Loan sharks charge interest rates daily, and if gangsters fail to repay their debts on time, the consequences will be very serious.
Unable to repay his debts, Tony Manning loaded a bullet into his revolver, preparing to end it all and meet his maker.
It was Muller who saved Manning's life; Muller helped Manning pay off his debts.
Muller spent all his money on this and sold one of his two limited-edition classic cars.
Manning, having no way to repay Muller's kindness, vowed to give his life and faith in return.
The "Muller -Manning theorem" was proposed during this period, and Manning played a significant role in the conjecture and proof of the theorem, demonstrating exceptional initiative.
Then Muller went on a business trip to Europe, but the meeting was canceled halfway through, so Muller returned to the United States early.
Upon opening the door, Muller found his wife and Manning engaged in a passionate encounter in the living room, so passionate that the sofa cushions were torn to shreds...
"The room reeked of a suffocating filth, and I wanted to kill them both and then commit suicide." Decades later, Muller still harbors resentment. "But I ultimately didn't kill them. I left the United States and returned to Germany, where I found a new job at the University of Bonn."
"Damn it, Manning, that damned bastard! That ungrateful scumbag, he deserves to go to hell!" Shen Qi slammed his fist on the table in anger, finally understanding this part of History of Mathematics.
A wealthy and loyal German middle-class scholar keeps an ungrateful American son who is proficient in all sorts of vices, including eating, drinking, gambling, and whoring.
In summary, I, Muller, treated you, Manning, like a brother, helped you pay off your gambling debts, and saved you from the tragic fate of being tied up by the underworld and thrown into the Atlantic Ocean to feed the fish. Yet you, Manning, slept with my wife and tore up my sofa cushions.
Upon returning to Germany, Muller married a divorced German accountant; both were in their second marriages.
"My wife is very good and gentle now, so let bygones be bygones." After recounting that stimulating period of history with a sense of grief and indignation, Muller regained his composure.
"I am sorry to hear this, Professor Muller." Shen Qi felt sorry for Professor Muller, but was also grateful that Professor Muller shared this unforgettable experience that had made him contemplate suicide.
This shows that Professor Muller did not consider Shen Qi an outsider. It takes a lot of courage to talk about being cheated on by one's best friend, and one that would only be told to a close confidant.
"Shen Qi, you must never get involved in gambling, otherwise I will not acknowledge me as your mentor," Muller solemnly warned Shen Qi.
"I have absolutely no interest in any form of gambling. Don't worry, I will never touch this stuff in my life," Shen Qi said solemnly.
Muller nodded with satisfaction. "Good boy, let's now discuss the reproof of the 'Muller -Shen Theorem' in detail."
"Okay, let's begin now."
Strictly speaking, the "Muller -Shen theorem" can only be called the "Muller -Shen hypothesis" at this stage.
Everyone has the right to make any kind of assumption or conjecture and publish it on the world's largest public website.
"I predict that there must be life on a planet 3.28 million light-years away from Earth. They have physical structures and civilizations similar to humans, and we can become friends."
This is just a hypothesis proposed by a 13-year-old high school student in Ohio, USA, and posted on his Mom's Twitter account, attracting a lot of followers to view and like it.
If scientists cannot provide strong evidence to refute the high school students' conjecture, then that conjecture will persist until it is proven or disproven.
However, scientists wouldn't take a high school student's conjecture seriously; such a conjecture has no academic value and is difficult to verify with current experimental equipment.
Scientists' attitude towards wildly imaginative, seemingly absurd, worthless conjectures proposed by unknown individuals that cannot be verified by existing theories or equipment is mostly: you can make any conjecture you want, but if I take it seriously, I'll lose.
Scientists often pay attention to conjectures or hypotheses proposed by renowned scholars that are professional, logically supported, academically valuable, and theoretically verifiable at the current stage, and then conduct verification.
The "Muller -Manning theorem" is professional, logical, and has certain academic value. It was first proposed jointly by Muller and Manning.
According to Shen Qi, the three assertions of the "Muller -Manning theorem" are theoretically valid, but the reason why it has not been recognized by the IMU for more than 30 years is because there are flaws in the proof.
Something exciting happened between Muller, Manning, and Muller's ex-wife, and Muller and Manning have not seen each other for over thirty years.
Therefore, the revision of the "Muller -Manning theorem" was interrupted, spanning a century, and was delayed until the 21st century.
The late Manning has been blacklisted by Muller, and Shen Qi has now taken Manning's place to complete the follow-up work.
The "Muller -Shen Theorem" adopts the three propositions of the "Muller -Manning Theorem" verbatim, and its core work is to use 21st-century mathematical methods to complete a rigorous proof.
More than 30 years have passed. Mathematics has progressed, classical theories remain classic, but specific processing methods are being updated and replaced.
After a week of discussion, Shen Qi believes that the definition of approximation tightness should be redefined.
This is the premise, the foundation, and the weapon.
Muller agreed with Shen Qi's line of thinking; he seemed to have rediscovered the passion he had when he was engrossed in his studies.
"Recalling the history and related definitions of approximation compactness, this definition was first proposed by Jeffimov. As a property of Banach space, it can guarantee that for any x∈X, there is an optimal approximation element in a non-empty closed convex set." Shen Qi searched through a bunch of literature, and while doing professional research, he also sorted out the History of Mathematics in a more in-depth and detailed way.
Shen Qi has always wanted to write a History of Mathematics, believing it to be a very meaningful endeavor.
However, due to limited skill and insufficient experience, Shen Qi is currently still in the stage of conceptualizing, learning, and accumulating knowledge.
Compared to the vast array of professional mathematics textbooks, there are far too few books related to the History of Mathematics. Truly classic reference books on the History of Mathematics can be counted on one hand.
The most classic History of Mathematics, widely recognized in the field, is "Mathematical Thought from Ancient to Modern Times" written by the American Klein, Shen Qi acknowledges the academic status of this History of Mathematics.
However, Klein's History of Mathematics is not suitable for people outside of mathematics professionals. Sun Yat-sen University the content consists of advanced mathematical theories, which may be incomprehensible even to the Mathematics Department students with poor grades.
Shen Qi's ambition is to write a History of Mathematics that is both profound and easy to understand, as well as engaging and interesting.
Chinese people who score 100 or above in the National College Entrance Examination (Gaokao) mathematics (out of a possible 150) should be able to understand half of Shen's History of Mathematics.
Anyone who hasn't failed Advanced Mathematics in college should be able to understand about 90% of the content in Shen's History of Mathematics.
Even if one knows nothing about mathematics, as long as one can read, one should be able to understand one-fifth of the content of Shen's History of Mathematics.
This is Shen Qi's vision for a widely circulated History of Mathematics, and he hopes to accomplish this meaningful task.
"That's right. I remember that in the late 70s and early 80s, Magnusson proved that X is locally uniformly convex at its midpoint if and only if the closed sphere of X is an approximate compact Chebyshev set." Professor Muller pulled Shen Qi back to reality from history.
"It was during that period that you, Professor Muller, proved that if C is an approximate compact set, then the projection operator is upper semi-continuous," Shen Qi said.
"Yes, that was probably the only valuable thing I did at the time. But it was useless; the other arguments couldn't be effectively connected, so the IMU never recognized the theorem I proposed in 1982." When he was in his sixties, Muller summarized his performance in his thirties, which can be summed up as a lack of experience among young people.
"Therefore, based on Professor Muller's proof, I boldly propose a new definition. Please see..." Shen Qi handed a blank sheet of paper to Muller.
After reviewing Shen Qi's manuscript, Muller stated with great certainty, "I believe the IMU will recognize the 'Muller -Shen Theorem' within three months."
"Perhaps it should be called the 'Shen- Muller Theorem, Shen Qi, your contribution is even greater," Professor Muller added.